Limited Population Growth

Part 4: Fruit Flies: Automating the Process

We will study the growth of the fruit fly population over the time period from 0 to 100 days, using a variety of time intervals Delta-t. To do so, we will simply specify n, the number of equal time intervals that we wish to create from [0, 100] . Then Delta-t = 100/n. We start with n = 20.

1. Enter formulas defining n and Delta-t. Why is the starting value of Delta-t the same as in Part 3?
2. Delta-t is the distance between consecutive t values. Fill in the appropriate values in the following list.
• t₀ = ___
• t₁ = ___
• t₂ = ___
• t₃ = ___
3. Write a formula for t_k in terms of k and Delta-t. This formula should give the correct values for t_k for k = 0, 1, ... , n. Complete and enter the command in your worksheet to define t as a function of k.
4. Enter the commands in your worksheet to compute p_k and slope_k in terms of k and Delta-t. Note that p_k is computed recursively, that is, p_k is defined in terms of p_k-1.
5. Plot p_k as a function of t_k. Do the population values vary in the way you expected? Explain.
6. Plot slope_k as a function of t_k. Do the slope values vary in the way you expected? Explain.
7. What population size does this simulation predict for day 20? for day 100?

In the next Part we will study what happens when the time interval is subdivided into more pieces -- besides just having more points on the curves.

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Last modified: September 23, 1997